There are several possibilities for managing tab groups.

To create a new tab group, you can right-click on a tab title and select Move to New Tab Group.

Keyboard shortcuts are available too.

The tab groups will be placed into two panes that can be resized. It is an horizontal split: the original tab group is on the left, the new tab group is added on the right.

You can open as much tab groups in a gedit window as your screen allows, but you will have to resize them in order to see them correctly.

You can drag and drop a tab into another tab group.

See Drag and drop tabs for more details.